Hello again. I found that I couldn't use the exit door in level 6, I had to create a fall in the right room to get the game to progress. Is there a way to fix this? Will removing the room allow me to use an exit door? Further, am I going to have the same issue between level 12a and 12b?

If you cannot enter an opened exit door, it's usually because it's in the room where the prince starts. If you cannot open an exit door, it's usually because the button (event) doesn't point to the left half of the exit. If it's something else you ran into, you could either give a more detailed description of the problem, or private message LEVELS.DAT to someone to look at it.

If you press F2 on the main screen you can modify some PRINCE.EXE settings.

If "Allow triggering of any tile" is enabled (on "Y"), buttons can also make loose floors fall down.
Used in, for example, level 7 of my Micro Palace.
You can watch the video (you can hear the tiles fall) or try the level yourself (ZIP; start level 7 with "2.exe megahit 7").

I found that I couldn't use the exit door in level 6, I had to create a fall in the right room to get the game to progress. Is there a way to fix this?

How do you mean "couldn't use the exit door"?

If you open an exit door on level 6 after you have seen the shadow, the exit door gets stuck in the opening animation.
You can enter the exit door, but the game won't load the next level, unless you press Ctrl+A.
A fix is mentioned here: viewtopic.php?p=16581#p16581